计算Pascal三角形深对角线的算法

Question

鉴于Pascal三角形的深对角线：

          1
        1   1
      1   2   1
    1   3   3   1
  1   4   6   4    1
1   5   10  10   5   1

1st diagonal: 1 1 1 1 1 ...
2nd diagonal: 1 2 3 4 5 ...
3rd diagonal: 1 3 6 10 15 ...
4th diagonal: 1 4 10 20 35 ...

是否存在从任何第i个对角线计算前k个项的算法？

Answer 1

是的，维基百科涵盖了这一点。你走了：

http://en.wikipedia.org/wiki/Pascal%27s_triangle#Calculating_a_row_or_diagonal_by_itself